MathDB

13

Part of 1992 Baltic Way

Problems(1)

Inequality with 2n variables

Source: Baltic Way 1992 #13

2/18/2009
Prove that for any positive x1,x2,…,xn,y1,y2,…,yn x_1,x_2,\ldots,x_n,y_1,y_2,\ldots,y_n the inequality \sum_{i\equal{}1}^n\frac1{x_iy_i}\ge\frac{4n^2}{\sum_{i\equal{}1}^n(x_i\plus{}y_i)^2} holds.
inequalitiesinequalities proposed